1. Technical Field
Example embodiments of the present invention relate to methods for forming a pattern and masks, and more particularly, to methods for forming a pattern using an electron beam and cell masks used in electron beam lithography.
2. Description of the Related Art
Electron beam lithography may be used to form a material layer on the surface of a substrate and to pattern the material layer. That is, electron beam lithography may include applying electron beam resist on the material layer, irradiating (or writing) the material layer with an electron beam along a pattern, developing the electron beam resist, and etching the material layer by using the electron beam resist pattern as a mask. Electron beam lithography may be used to directly form a material layer for an integrated circuit on the substrate, but typically is used when manufacturing a photo mask for photolithography.
A conventional method of manufacturing a photo mask is described in detail with reference to FIG. 1. The conventional method may include applying electron beam resist 130 on a shielding layer 120 formed on the entire surface of a transparent substrate 110, irradiating a pattern with an electron beam 150, developing the electron beam resist to form a resist pattern by using a solubility difference varying according to the electron beam irradiating, and etching the shielding layer 120 using the formed resist pattern as a mask.
However, the electron beam 150 exposes not only a desired region of the electron beam resist 130, but also an undesired region of the electron beam resist 130. An undesired region of the electron beam resist 130 may be exposed because the electron beam 150 reflects from the surface of the shielding layer 120, collides with atoms of the electron beam resist material and scatters inside the electron beam resist 130. This scattering 170 is referred to herein as forward scattering and backward scattering. Further, re-scattering 160 may occur because the electron beam reflects from the inside or surface of the electron beam resist 130 to the bottom surface of an objective lens 140 of an electron beam irradiator and from the bottom surface of the objective lens back to the electron beam resist 130.
Due to scattering 170 and re-scattering 160, the electron beam resist may be exposed up to a distance of 10 cm away from a portion targeted by the electron beam (i.e., a distance up to 10 cm away from an edge of the pattern). Forward scattering and backward scattering may be responsible for additional exposure up to about 10 μm, which may result in an undesired region of exposed electron beam resist 130. Also, the re-scattering may be responsible for additional exposure up to about 10 mm, which may result in an undesired region of exposed beam resist 130. The additional exposure may deteriorate the accuracy of the shield layer pattern, and may cause a change in critical dimension (CD). A change in the CD resulting from the additional exposure by the forward scattering and backward scattering is defined as a proximity effect, and the change in the CD resulting from the additional exposure by the re-scattering is defined as re-scattering effect, multiple scattering effect or fogging effect of the electron beam. When exposure is performed using the electron beam at a dose of about 8 μC/cm2 and at an accelerating voltage of about 10 keV, the change in the CD of the photo mask because of the re-scattering effect of the electron beam may be about 10˜20 nm, and this may significantly affect the manufacture of integrated circuits for high integration.
In a conventional method of reducing fogging effect, an absorption plate including grooves formed in a honeycomb pattern may be attached onto the lower surface of the objective lens 140 to absorb the re-scattered electron beam. However, because this conventional method cannot absorb all of the re-scattered electrons, this conventional method is limited in reducing the fogging effect.
FIG. 2 illustrates a conventional method for correcting the proximity effect of the backward scattering. FIG. 3 illustrates an intensity log slope at a patterning position in each pattern of FIG. 2.
FIGS. 2 and 3 will be referred to describe a method of artificially controlling a local dose of electrons to remove CD errors, which may result from dose variation between an isolated space pattern, a line and space pattern and an isolated line pattern. If the backward scattering range is sufficiently larger than the pattern size, a dose value may be determined by using the electron beam open ratio U of the pattern. The open ratio U of an isolated space pattern is about 0, and the open ratio U of the line and space pattern is ½ when the line to space ratio is 1:1. The open ratio U of the isolated line pattern is about 1. That is, the isolated line pattern is more exposed to the electron beam than the isolated space pattern and the line and space pattern.
FIG. 2 illustrates theoretical patterns and energy distributions before and after correcting the proximity effect with respect to the patterns. If the patterns are irradiated at the same dose as shown by the energy distribution before correcting the proximity effect, the isolated space pattern, the line and space pattern, and the isolated line pattern have different energy values. The energy values of the patterns are different because the total amount of backward scattering affecting each pattern varies with the open ratio U.
The total amount of the backward scattering equals the backward scattering coefficient η times the open ratio U. Thus, for the isolated space pattern where the open ratio U is about 0, the total amount of the backward scattering is about 0. For the line and space pattern where the open ratio U is about 1/2, the total amount of the backward scattering is about η/2. For the isolated line pattern where the open ratio U is about 1, the total amount of the backward scattering is about η. Consequently, in the isolated space pattern, the line and space pattern and the isolated line pattern are changed into about 1/2, about 1/2+1/2η and about 1/2+η, respectively, by the proximity effect. In order to equalize the dose values for patterning, the isolated space pattern and the line and space pattern may be irradiated at a corrected dose Dp for correcting the proximity effect. The corrected dose Dp may be represented as the following Equation (1):Dp=(1/2+η)/(1/2+ηU)   (1)As described above, irradiating the isolated space pattern and the line and space pattern at the corrected dose Dp may equalize the energy values for patterning. Equalizing the energy values may result in the CD values of the patterns being substantially uniform. However, this conventional method may substantially equalize the CD values but may also decrease a dose margin by the backward scattering.
FIG. 3 illustrates a formula of an intensity log slope (ILS) representing the dose margin by the backward scattering. In a typical electron beam lithography, the backward scattering coefficient η is about 0.5, wherein the ILS of the isolated line pattern having the open ratio U of about 1 decreases by about half relative to the isolated space pattern having the open ratio U of about 0. The ILS of the 1:1 line and space pattern having the open ratio of 1/2 is about 2/3 relative to the isolated space pattern.
That is, because a conventional method of correcting the proximity effect decreases the dose margin by the backward scattering as in the isolated line pattern, the conventional method is limited in equalizing the CD. Thus, it is important to decrease an absolute amount of the backward scattering. Consequently, in the electron beam lithography, it is important to decrease all of the forward scattering, backward scattering and re-scattering.